An empirical method for describing the joint effects of environmental and other variables on crop yield

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Abstract
Summary: There is considerable interest in developing understanding of the spatial variation of crop yield within fields in relation to the spatial variation of environmental factors. Such understanding might allow inputs to crops to be used more efficiently by spatially variable application. The joint action of factors on crop yield (whether controlled treatments or environmental variables) may be additive, interactive or potentially limiting in the sense of von Liebig's “Law of the Minimum”. The nature of the joint action of an input and environmental factors has profound implications for the possibility of improving the efficiency of use of the input by spatially variable application. Conventional methods for analysing data on such factors and yield (e.g. multiple regression) make specific assumptions compatible only with a narrow range of permissible models. A procedure is proposed and demonstrated in this paper for the exploratory analysis of data from experiments and/or crop surveys in order to describe the joint action of important factors on crop yield. The procedure could be applied to specific experiments in order to indicate whether there is any scope for optimising rates of an input with respect to one or more spatially variable factors, and for indicating whether the relationship between the local optimum rate of the input and values of these factors is simple (factors act additively or in accordance with the Law of the Minimum) or complex (factors interact).

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